基于高斯谢尔模型光源模型及柯林斯衍射积分公式，通过近似求解得到了随机电磁光束通过像散光学系统传输后其偏振度保持恒定的充分条件。解析结果及数值模拟仿真结果均显示，当光学系统像散系数足够大且与光源参数存在一定的制约关系时，光束传输后参考平面处偏振度保持恒定并且与光源处初始偏振度相同。该充分条件的成立性不受光学系统元素及传输距离等其他因素的制约，因此具有一定的独立性。该充分条件对于光学系统偏振成像及光路偏振探测等实际应用工程具有潜在的理论参考价值。

Based on the theory of Gaussian-Schell model source and Collins diffraction integral formula, the sufficient condition for invariant polarization of stochastic electromagnetic beams through astigmatic optical systems is derived. Both analytical and simulated results indicate that, when the astigmatic coefficient of optical systems is large enough and it satisfies certain restrictive condition with source parameters, degree of polarization of beams will keep invariant in propagation. As a result, the propagating degree of polarization is as the same as its initial value in the source plane. This sufficient condition is sole, and it is independent of optical systems′ elements and propagation distance, etc. The results may provide potential merits and applications in polarization imaging and detecting in optical systems.